A distributed adaptive scheme for multiagent systems

In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known, and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multiagent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multiagent systems. In this scheme, asymptotic consensus of a second-order uncertain multiagent system is achieved in a network of directed graph.